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On the Optimal Policy for Deterministic and Exponential Polling Systems

Author

Listed:
  • Bruno Gaujal

    (INRIA Rhône-Alpes, Montbonnot Saint Martin, France)

  • Arie Hordijk

    (Dept of Mathematics, Leiden University, Leiden)

  • Dinard van der Laan

    (Dept of Econometrics & Operations Research, Vrije Universiteit Amsterdam)

Abstract

In this paper, we consider deterministic (both fluid and discrete) polling systems with N queues with infinite buffers and we show how to compute the best polling sequence (minimizing the average total workload). With two queues, the best polling sequence is always periodic when the system is stable and forms a regular sequence. The fraction of time spent by the server in the first queue is highly non continuous in the parameters of the system (arrival rate and service rate) and shows a fractal behavior. Convexity properties are shown in Appendix as well as a generalization of the computations to the stochastic exponential case.

Suggested Citation

  • Bruno Gaujal & Arie Hordijk & Dinard van der Laan, 2005. "On the Optimal Policy for Deterministic and Exponential Polling Systems," Tinbergen Institute Discussion Papers 05-066/4, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:20050066
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    References listed on IDEAS

    as
    1. Arie Hordijk & Dinard van der Laan, 2004. "The unbalance and bounds on the average waiting time for periodic routing to one queue," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 59(1), pages 1-23, February.
    2. Arie Hordijk & Dinard van der Laan, 2004. "Periodic routing to parallel queues and billiard sequences," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 59(2), pages 173-192, June.
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    More about this item

    Keywords

    Polling systems; regular sequences; multimodularity; optimal control;
    All these keywords.

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools

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